Problem: $\dfrac{d}{dx}\left(\dfrac{3}{x^6}-\dfrac{1}{x^4}+5\right)=$
Solution: The strategy We can first rewrite each rational term in the expression as a negative power of $x$. Then, the derivatives of these terms can be found using the power rule : $\dfrac{d}{dx}(x^n)=n\cdot x^{n-1}$ (Remember that this applies even when $n$ is negative.) Rewriting rational terms as negative powers $\begin{aligned} &\phantom{=}\dfrac{3}{x^6}-\dfrac{1}{x^4}+5 \\\\ &=3x^{-6}-x^{-4}+5 \end{aligned}$ Differentiating using the power rule $\begin{aligned} &\phantom{=}\dfrac{d}{dx}(3x^{-6}-x^{-4}+5) \\\\ &=3\dfrac{d}{dx}(x^{-6})-\dfrac{d}{dx}(x^{-4})+\dfrac{d}{dx}(5) \\\\ &=3 (-6x^{-7})-(-4)x^{-5}+0 \\\\ &=-18x^{-7}+4x^{-5} \\\\ &=-\dfrac{18}{x^7}+\dfrac{4}{x^5} \end{aligned}$ In conclusion, $\dfrac{d}{dx}\left(\dfrac{3}{x^6}-\dfrac{1}{x^4}+5\right)=-\dfrac{18}{x^7}+\dfrac{4}{x^5}$.